Problem: Rewrite as a simplified fraction. ${2.50\overline{1} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2501.1111...\\ 100x &= 250.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2251}$ ${x = \dfrac{2251}{900}} \text{or} {2 \dfrac{451}{900}}$